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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 4400.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.ba1 | 4400x2 | \([0, -1, 0, -1688, -26128]\) | \(1039509197/484\) | \(247808000\) | \([2]\) | \(2304\) | \(0.56690\) | |
4400.ba2 | 4400x1 | \([0, -1, 0, -88, -528]\) | \(-148877/176\) | \(-90112000\) | \([2]\) | \(1152\) | \(0.22032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4400.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 4400.ba do not have complex multiplication.Modular form 4400.2.a.ba
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.